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Evaluate the following improper integrals with infinite limits on the basis of their definition : (a) int_(2)^(oo)(xdx)/(sqrt((x^(2)-3)^(3))), (b) int_(1)^(oo)(dx)/(x+x^(3)), (c ) int_(0)^(oo)(xdx)/(sqrt((4x^2+1)^(3))), (d) int_(1)^(oo)(dx)/(x^(2)(1+x)), (e) int_(-oo)^(oo)(dx)/(x^(2)-6x+10), (f) int_(0)^(oo)e^(-x)sinxdx |
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Answer» (C ) `1;` (d) `1-1n2;` (e ) `pi;(F)(1)/(2)`. |
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